We have been given that the population of a certain species of fish has a growth rate of 2.2% per year. It is estimated that the the current population is 350,000.
We are asked to find the time it will take the fish population to reach 1,000,000.
We will use exponential growth formula to solve our given problem.
An exponential growth function is in form [tex]y=a\cdot (1+r)^x[/tex], where,
y = Final amount,
a = Initial amount,
r = Growth rate in decimal form,
x = Time
[tex]2.2\%=\frac{2.2}{100}=0.022[/tex]
[tex]y=350,000\cdot (1+0.022)^x[/tex]
To find the time for the fish population to reach 1,000,000, we will substitute [tex]x=1,000,000[/tex] in our equation as:
[tex]1,000,000=350,000\cdot (1+0.022)^x[/tex]
[tex]1,000,000=350,000\cdot (1.022)^x[/tex]
[tex]\frac{1,000,000}{350,000}=\frac{350,000\cdot (1.022)^x}{350,000}[/tex]
[tex]2.8571428571428571=(1.022)^x[/tex]
Now we will take natural log on both sides:
[tex]\text{ln}(2.8571428571428571)=\text{ln}((1.022)^x)[/tex]
[tex]\text{ln}(2.8571428571428571)=x\cdot \text{ln}(1.022)[/tex]
[tex]x=\frac{\text{ln}(2.8571428571428571)}{\text{ln}(1.022)}[/tex]
[tex]x=\frac{1.0498221244986776733}{0.0217614917815127}[/tex]
[tex]x=48.2421947[/tex]
Upon rounding to nearest tenth, we will get:
[tex]x\approx 48.2[/tex]
Therefore, it will take approximately 48.2 years for the fish population to reach 1,000,000.
Answer:
47.7
Step-by-step explanation:
right answer
Solve the problem. A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time is less than 8.9 hours.
Consider the following sets of sample data:
A:
$36,900
, $19,400, $22,200, $21,900, $35,300, $20,500, $35,400, $24,000, $37,700, $35,300, $38,300, $29,600, $26,000, $38,400
B:
2.1
, 5.0, 3.5, 3.7, 2.5, 2.1, 3.7, 4.6, 2.7, 4.1, 1.7
For each of the above sets of sample data, calculate the coefficient of variation, CV. Round to one decimal place.
Answer:
The coefficient of variation for A is 24.6%.
The coefficient of variation for B is 33.7%.
Step-by-step explanation:
The coefficient of variation (CV) is well defined as the ratio of the standard deviation to the mean. It exhibits the degree of variation in association to the mean of the population.
The formula to compute the coefficient of variation is,
[tex]CV=\frac{SD}{Mean}\times 100\%[/tex]
Consider the data set A.
Compute the mean of the data set A as follows:
[tex]Mean_{A}=\frac{1}{n}\sum X[/tex]
[tex]=\frac{1}{14}\times [36900+19400+...+26000+38400]\\=30064.2857[/tex]
Compute the standard deviation of the data set A as follows:
[tex]SD_{A}= \sqrt{ \frac{ \sum{\left(x_i - Mean_{A}\right)^2 }}{n-1} }[/tex]
[tex]= \sqrt{ \frac{ 712852142.8571 }{ 14 - 1} } \\\approx 7405.051[/tex]
Compute the coefficient of variation for A as follows:
[tex]CV=\frac{SD_{A}}{Mean_{A}}\times 100\%[/tex]
[tex]=\frac{7405.051}{30064.2857}\times 100\%\\=24.6\%[/tex]
The coefficient of variation for A is 24.6%.
Consider the data set B.
Compute the mean of the data set B as follows:
[tex]Mean_{B}=\frac{1}{n}\sum X[/tex]
[tex]=\frac{1}{11}\times [2.1+5.0+...+4.1+1.7]\\=3.2455[/tex]
Compute the standard deviation of the data set B as follows:
[tex]SD_{B}= \sqrt{ \frac{ \sum{\left(x_i - Mean_{B}\right)^2 }}{n-1} }[/tex]
[tex]= \sqrt{ \frac{ 11.9873 }{ 11 - 1} } \\\approx 1.0949[/tex]
Compute the coefficient of variation for B as follows:
[tex]CV=\frac{SD_{B}}{Mean_{B}}\times 100\%[/tex]
[tex]=\frac{1.0949}{3.2455}\times 100\%\\=33.7\%[/tex]
The coefficient of variation for B is 33.7%.
Angela wants to celebrate her birthday by eating pizza with her friends. She wants to buy
one box of pepperoni pizza for $9.50 and c boxes of cheese pizza for $8.50 each. Write an
expression, in dollars, that represents the amount Angela will spend on pizzas for her
birthday celebration.
Answer:
$8.50C + $9.50 = ______
That's the expression.
Which of the following are true if events A and B are independent? Select all that apply.
A. P(A | B) = P(A)
B. P(A | B) = P(B)
C. P(A | B) = P(A and B)
D. P(B | A) = P(A and B)
E. P(B | A) = P(A)
F. P(B | A) = P(B)
Answer:
The correct statement are (A) and (F).
Step-by-step explanation:
Events A and B are independent or mutually independent events if the chance of their concurrent happening is equivalent to the multiplication of their distinct probabilities.
That is,
[tex]P(A\cap B)=P(A)\times P(B)[/tex]
The conditional probability of event A given B is computed using the formula:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
And the formula for the conditional probability of event B given A is:
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]
Consider that events A and B are independent.
Then the conditional probability of event A given B will be:
[tex]P(A|B)=\frac{P(A\cap B)}{P(B)}[/tex]
[tex]=\frac{P(A)\times P(B)}{P(B)}\\\\=P(A)[/tex]
And the conditional probability of event B given A will be:
[tex]P(B|A)=\frac{P(A\cap B)}{P(A)}[/tex]
[tex]=\frac{P(A)\times P(B)}{P(A)}\\\\=P(B)[/tex]
Thus, the correct statement are (A) and (F).
In the context of independent events, the correct statements are that P(A | B) = P(A) and P(B | A) = P(B), indicating that the occurrence of one event does not affect the probability of the other event occurring. Other options presented do not accurately represent the properties of independent events in probability.
Explanation:When assessing whether events A and B are independent, it is essential to understand the criteria for independence in probability theory. Specifically, two events are independent if the probability of one event occurring does not affect the probability of the other event occurring. This can be mathematically represented as follows: P(A AND B) = P(A)P(B), P(A|B) = P(A), and P(B|A) = P(B).
If events A and B are independent, the correct statements among the choices provided are:
Option A is true because if A and B are independent, the probability of A occurring given that B has occurred is the same as the probability of A occurring on its own.
Option F is also correct for the same reason applied to event B; the probability of B occurring given that A has occurred is the same as the probability of B occurring on its own.
The remaining options are incorrect because they do not align with the definition of independent events:
Area of the base = 75 square inches and
height is 15 inches
The question pertains to calculating the volume of a triangular prism using the given area of the base and height. The volume is found by multiplying the area of the base (75 square inches) by the height (15 inches) to yield an answer of 1125 cubic inches.
Explanation:The question provided relates to the concept of finding the volume of a geometric shape, specifically a triangular prism, as it gives the area of the base and the height of the prism. In geometry, to find the volume of a triangular prism, we use the formula V = Area of base imes Height. Given that the area of the base provided is 75 square inches and the height is 15 inches, we can calculate the volume of the triangular prism.
To calculate volume:
Multiply the area of the base (75 square inches) by the height of the prism (15 inches).Volume = 75 in2 imes 15 in = 1125 cubic inches.Thus, the volume of the triangular prism is 1125 cubic inches.
Solve 15y − 1 = 11/2y + 2
Answer:
y = 6/19 = 0.316
Step-by-step explanation:
:)
Answer:
y=6/19
Step-by-step explanation:
15y − 1 = 11/2y + 2
15y-11/2y=3
30/2y-11/2y=3
19/2y=3
19y=6
y=6/19
The compressive strength of concrete is normally distributed with mu = 2500 psi and sigma = 50 psi. A random sample of n = 8 specimens is collected. What is the standard error of the sample mean?
Round your final answer to three decimal places (e.g. 12.345).
The standard error of the sample mean is __ psi.
Answer:
The standard error of the sample mean is _17.677_ psi.
Step-by-step explanation:
Explanation:-
A random sample of n = 8 specimens is collected.
Given sample size is n = 8
Given mean of the population 'μ' = 2500 psi
standard deviation 'σ' = 50 psi
Let x⁻ is the mean of the observed sample
Standard error of the sample mean = [tex]\frac{S.D}{\sqrt{n} }[/tex] ...(i)
Given Population of standard error (S.D) 'σ' = 50 psi
Now substitute all values in (i)
[tex]S.E = \frac{50}{\sqrt{8} } =17.677[/tex]
Conclusion:-
The standard error of the sample mean is _17.677psi.
The standard error of the sample mean for a sample of 8 concrete specimens is approximately 17.68 psi
To calculate the standard error of the sample mean, we use the formula:
[tex]\[ \text{Standard Error} = \frac{\sigma}{\sqrt{n}} \][/tex]
Where:
- [tex]\sigma[/tex] is the standard deviation of the population.
- n is the sample size.
Given:
- [tex]\sigma[/tex] = 50 psi
- n = 8
Substituting these values into the formula:
[tex]\[ \text{Standard Error} = \frac{50}{\sqrt{8}} \][/tex]
[tex]\[ \text{Standard Error} = \frac{50}{2.828} \][/tex]
[tex]\[ \text{Standard Error} \approx 17.68 \][/tex]
So, the standard error of the sample mean is approximately 17.68 psi.
describe the products you get if you multiply 8 by factors less than 1. describe the products you get if you multiply 8 by factors greater than 1. give some examples that justify your answer
Answer:
When you multiply 8 by factors less than 1, your product is a number less than 8. An example of this would be when you multiply 8 by 1/2. Your product is 4. Another example is when you multiply 8 by 1/4. Your product is 2. When you multiply 8 by factors that are greater than 1, your product is a number greater than 8. One example of this is when you multiply 8 by 5. Your answer is 40. Another example is when you multiply the number 8 by 2. Your product is 16.
Step-by-step explanation:
Final answer:
When you multiply 8 by factors less than 1, the products will be smaller than 8. When you multiply 8 by factors greater than 1, the products will be larger than 8.
Explanation:
When you multiply 8 by factors less than 1, the products will be smaller than 8. For example, if you multiply 8 by 0.5, you get a product of 4. The further the factor is from 1, the smaller the product will be. Some other examples include multiplying 8 by 0.25 to get a product of 2, or multiplying 8 by 0.1 to get a product of 0.8.
On the other hand, when you multiply 8 by factors greater than 1, the products will be larger than 8. For example, if you multiply 8 by 2, you get a product of 16. The further the factor is from 1, the larger the product will be. Some other examples include multiplying 8 by 3 to get a product of 24, or multiplying 8 by 10 to get a product of 80.
What is the following product? RootIndex 5 StartRoot 4 x squared EndRoot times RootIndex 5 StartRoot 4 x squared EndRoot 4 x squared RootIndex 5 StartRoot 16 x Superscript 4 Baseline EndRoot 2 (RootIndex 5 StartRoot 4 x squared EndRoot) 16 x Superscript 4
Answer:
[tex](B)\sqrt[5]{16x^4}[/tex]
Step-by-step explanation:
We are required to evaluate:
[tex]\sqrt[5]{4x^2} X \sqrt[5]{4x^2}[/tex]
By laws of indices: [tex]\sqrt[n]{x}=x^{^\frac{1}{n} }[/tex]
Therefore: [tex]\sqrt[5]{4x^2} =(4x^2)^{^\frac{1}{5}[/tex]
Thus:
[tex]\sqrt[5]{4x^2} X \sqrt[5]{4x^2}=(4x^2)^{1/5}X(4x^2)^{1/5}\\$Applying same base law of indices:a^mXa^n=a^{m+n}\\(4x^2)^{1/5}X(4x^2)^{1/5}=(4x^2)^{1/5+1/5}=(4x^2)^{2/5}\\$Now, by index product law: a^{mn}=(a^m)^n\\(4x^2)^{2/5}=[(4x^2)^2]^{1/5}=[16x^4]^{1/5}\\[/tex]
[tex][16x^4]^{1/5}=\sqrt[5]{16x^4} \\$Therefore:\\\sqrt[5]{4x^2} X \sqrt[5]{4x^2}=\sqrt[5]{16x^4}[/tex]
Answer:
b in edge
Step-by-step explanation:
Brian has reduced his cholesterol level by 13% after his last check up. If his original level was 200, what is his cholesterol level now?
A 90% confidence interval for the mean height of students
is (60.128, 69.397). What is the value of the margin of error?
Answer:
4.635
Step-by-step explanation:
A confidence interval is:
CI = μ ± ME
where μ is the sample mean and ME is the margin of error.
In other words, the margin of error is half the width of the interval.
ME = (69.397 − 60.128) / 2
ME = 4.635
Solve the equation.
e + 1.2 =2
e=
Answer:
e= 0.8
Step-by-step explanation:
Get e by itself, so subtrct 1.2 from 2 to get 0.8
The solution to the equation [tex]\(e + 1.2 = 2\) is \(e = 0.8\).[/tex]
To solve the equation \(e + 1.2 = 2\), we need to isolate the variable \(e\) on one side of the equation. Here's how you can do it step by step:
1. **Subtract 1.2 from both sides:**
\[e + 1.2 - 1.2 = 2 - 1.2\]
\[e = 0.8\]
In the context of real numbers, this means that when you substitute \(e = 0.8\) back into the original equation, it holds true:
\[0.8 + 1.2 = 2\]
This equation verifies that \(e = 0.8\) is indeed the solution. In a broader sense, solving equations like this one is a fundamental concept in algebra and mathematics. It allows us to find unknown values in various real-life situations, making it a crucial skill in fields such as physics, engineering, economics, and many others.
Understanding how to manipulate equations helps us model and solve complex problems, making mathematics an essential tool in problem-solving and critical thinking.
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how many 1/2 are in 7
14
All you have to do is multiply the 1/2 by the 7.
Answer:
14
Step-by-step explanation:
there are 14 1/2 in 7
what is a area of a triangle with a heigt of 5 inches and a base of 10inches
Answer: 25 in²
Step-by-step explanation: To find the area of a triangle, start with the formula for the area of a triangle which is shown below.
[tex]Area =[/tex] [tex]\frac{1}{2} bh[/tex]
In this problem, we're given that the base is 10 inches
and the height is 5 inches.
Now, plugging into the formula, we have [tex](\frac{1}{2})(10in.)(5 in.)[/tex].
Now, it doesn't matter which order we multiply.
So we can begin by multiplying (1/2) (10 in.) to get 5 inches.
Now, (5 in.) (5 in.) is 25 in².
So the area of the triangle is 25 in².
Please help!!!
If the area of a rectangle is 42m^2, find value x
Answer:
Give me more fees back on your equation
Step-by-step explanation:
5/6 minus what equals 1/3
Answer:
3/6 = 1/2
Step-by-step explanation:
Important: 1/3 = 2/6
5/6-?=1/3
5/6-?=2/6
3/6=?
Someone please help
????????
Answer:
use the distance formula,
by using it, prove the adjacent sides of the quadrilateral DEFG
hence, DEFG would be a rhombus
Which expressions represent 1 less than the product of 3 and 4?
Answer:3+4-1
Step-by-step explanation:
The administration at Pierce College conducted a survey to determine the proportion of students who ride a bike to campus. Of the 125 students surveyed 6 ride a bike to campus. Which of the following is a reason the administration should not calculate a confidence interval to estimate the proportion of all students who ride a bike to campus? Check all that apply.
A. The sample needs to be random but we don’t know if it is.
B. The actual count of bike riders is too small.
C. The actual count of those who do not ride a bike to campus is too small.
D. n(p-hat) is not greater than 10.
E. n(1 minus p-hat) is not greater than 10.
Answer:
The correct option is (D).
Step-by-step explanation:
To construct the (1 - α)% confidence interval for population proportion the distribution of proportions must be approximated by the normal distribution.
A Normal approximation to binomial can be applied to approximate the distribution of proportion p, if the following conditions are satisfied:
[tex]n\hat p \geq 10[/tex][tex]n ( 1 - \hat p) \geq 10[/tex]In this case p is defined as the proportions of students who ride a bike to campus.
A sample of n = 125 students are selected. Of these 125 students X = 6 ride a bike to campus.
Compute the sample proportion as follows:
[tex]\hat p=\frac{X}{n}=\frac{6}{125}=0.048[/tex]
Check whether the conditions of Normal approximation are satisfied:
[tex]n\hat p =125\times 0.048=6<10\\n(1-\hat p) =125\times (1-0.048)=119>10[/tex]
Since [tex]n\hat p <10[/tex], the Normal approximation to Binomial cannot be applied.
Thus, the confidence interval cannot be used to estimate the proportion of all students who ride a bike to campus.
Thus, the correct option is (D).
11,235,000,000 in scientific notation
Answer:
the answer in scientific notation is 1.1235x10^10
An inverted pyramid is being filled with water at a constant rate of 35 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 6 cm, and the height is 8 cm. Find the rate at which the water level is rising when the water level is 3 cm.
Final answer:
The rate at which the water level is rising when the water level is 3 cm is approximately 2.92 cm/s.
Explanation:
To find the rate at which the water level is rising, we need to consider the volume of water being added per unit time and how that volume relates to the change in water level. The volume of a pyramid can be calculated using the formula V = (1/3)b*h, where b is the area of the base and h is the height. In this case, the base is a square with sides of length 6 cm, so the area is 6*6 = 36 cm^2. Substituting this into the formula, the volume of the pyramid is V = (1/3)*36*8 = 96 cm^3. Since the water is being filled at a rate of 35 cm^3/s, we can find the rate of the water level rising by taking the derivative of the volume equation with respect to time:
dV/dt = (1/3)*b*dh/dt
where dV/dt is the rate of change of volume, b is the area of the base, and dh/dt is the rate of change of the height (which is the same as the rate of change of the water level).
Substituting in the known values:
35 = (1/3)*36*(dh/dt)
dh/dt = (35*3)/(36) = 35/12 ≈ 2.92 cm/s
Which of the following explains how ΔAEI could be proven similar to ΔDEH using the AA similarity postulate?
Quadrilateral ABDC, in which point F is between points A and C, point G is between points B and D, point I is between points A and B, and point H is between points C and D. A segment connects points A and D, a segment connects points B and C, a segment connects points I and H, and a segment connects points F and G. Segments AD, BC, FG, and IH all intersect at point E.
∠AEI ≅ ∠DEH because vertical angles are congruent; reflect ΔHED across segment FG, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.
∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.
∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then dilate ΔHED to confirm segment ED ≅ segment EA.
∠AEI ≅ ∠DEH because vertical angles are congruent; reflect ΔHED across segment FG, then dilate ΔHED to confirm segment ED ≅ segment EI.
Answer:
∠AEI ≅ ∠DEH because vertical angles are congruent; rotate ΔHED 180° around point E, then translate point D to point A to confirm ∠IAE ≅ ∠HDE.
Step-by-step explanation:
tbh im not suuper sure but my educated guess is that by looking at it. Good Luck!
Two triangles are said to be similar by AA if two angles of both triangles are equal. The explanation that proves the similarity of [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex] by AA is option (a)
Given that: [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex]
To prove that [tex]\triangle AEI[/tex] and [tex]\triangle DEH[/tex] are similar by AA, it means that two corresponding angles of both triangles must be congruent. So, the following must be true:
The angle at point E in both triangles must be equal. i.e. [tex]\angle AEI \cong \angle DEH[/tex]. This is so because the angle at E is a vertical angle to both triangles, and vertical angles are congruent.The angle at A and D of both triangles must be equal, i.e. [tex]\angle IAE \cong HDE[/tex]. This is so because a 180 degrees rotation of [tex]\triangle DEH[/tex] around the center E will give a similar (but larger) triangle to [tex]\triangle AEI[/tex]. Point D can then be shifted to A.Hence, (a) is true
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The mean potassium content of a popular sports drink is listed as 138 mg in a 32-oz bottle. Analysis of 40 bottles indicates a sample mean of 136.9 mg. (a) State the hypotheses for a two-tailed test of the claimed potassium content.
Answer:
The value for p <0.1 i.e. 0.02088 that means ,we had success in test on potassium content
Step-by-step explanation:
Given:
Means: 138 mg
sample size =40
New mean=136.9 mg
To find : Hypothesis on test.
Solution:
We know that ,
Z=(X-mean)/standard deviation)/{(sqrt(sample size)}
Consider the standard deviation of 3.00 mg
Z=(136.9-138)/(3/sqrt(40))
=-1.1/0.4743
Z=-2.3192
two tailed test
=2{(1-p(<z))}
P value for Z=2.3192 is 0.98956
=2{1-0.98956}
=0.02088
The value for p <0.1
we had success in test on potassium content.
The hypothesis test for the sports drink's potassium content involves a null hypothesis (H0) that the mean is equal to the claimed 138 mg, and an alternative hypothesis (Ha) that it is not equal.
Explanation:The question involves conducting a hypothesis test for a sports drink's potassium content.
Establishing hypotheses for a two-tailed test involves setting a null hypothesis (H0) that the mean potassium content is equal to the claimed amount, and an alternative hypothesis (Ha) that the mean potassium content is not equal to the claimed amount.
Specifically:
H0: μ = 138 mg (The mean potassium content is 138 mg as listed.)Ha: μ ≠ 138 mg (The mean potassium content is not 138 mg as listed.)This is a basic procedure in statistical testing where the null hypothesis often represents a statement of 'no effect' or 'no difference', and the alternative hypothesis contradicts this assumption.
Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.8 years with a standard deviation of 0.7 years. (2 pts) Step 1. If a sampling distribution is created using samples of the ages at which 61 children begin reading, what would be the mean of the sampling distribution of sample means
Answer:
5.8 years
Step-by-step explanation:
The sampling distribution of the sample means has a mean that is equal to mean of the population from which the sample has been drawn.
study of elementary school students reports that the mean age at which children begin reading is 5.8 years with a standard deviation of 0.7 years.
This means the population mean is
[tex] \mu = 5.8 \: years[/tex]
and the population standard deviation is
[tex] \sigma = 0.7 \: years[/tex]
If a sampling distribution is created using samples of the ages at which 61 children begin reading, the mean of the sampling distribution of the sample mean will be
[tex]5.8 \: years[/tex]
The mean of the sampling distribution of sample means can be calculated by dividing the mean of the population by the square root of the sample size.
Explanation:To find the mean of the sampling distribution of sample means, we need to divide the mean of the population by the square root of the sample size. In this case, the mean of the population is 5.8 years and the sample size is 61 children. So, the mean of the sampling distribution of sample means can be calculated as:
Mean of sampling distribution of sample means = 5.8 years / sqrt(61) ≈ 0.745 years
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what is 4/7 divded by 10/21
Answer:
6/5
Step-by-step explanation:
(4/7) divided by (10/21) = (4/7) * (21/10) = (3*4)/10= 6/5
In a study of 346 comma 145 cell phone users, it was found that 26 developed cancer of the brain or nervous system. Assuming that cell phones have no effect, there is a 0.000113 probability of a person developing cancer of the brain or nervous system. We therefore expect about 40 cases of such cancer in a group of 346 comma 145 people. Estimate the probability of 26 or fewer cases of such cancer in a group of 346 comma 145 people. What do these results suggest about media reports that cell phones cause cancer of the brain or nervous system?
Answer:
a) P ( X ≤ 26 ) = 0.0134
b) The significance of the cell phone causing brain cancer is 1.34 or 0.0134
Step-by-step explanation:
Solution:-
- From the entire population of cell phone users os size N = 346,145 media reported n = 26 people who developed cancer of brain or nervous system.
- The probability of a person developing cancer of the brain or nervous system, assuming that cell phones have no effect, is p = 0.000113.
- Denote a random variable X: The number people who developed cancer of brain or nervous system are normally distributed.
- The expected or mean number of people who developed cancer of brain or nervous system are u = 40.
- The standard deviation ( s ) for the distribution would be:
[tex]s = \sqrt{u*( 1 - p ) }\\\\s = \sqrt{40*( 1 - 0.000113 ) }\\\\s = 6.3242\\[/tex]
- The random variate X follows normal distribution with parameters:
X ~ Norm ( 40 , 6.3242^2 )
- The probability of X ≤ 26 cases from the total population of N = 346,145 can be determined by evaluating the Z-score standard value of the test statistics:
[tex]P ( X \leq 26 ) = P ( Z \leq [ \frac{X - u }{s} ) \\\\P ( Z \leq [ \frac{ 26 - 40 }{6.3242} ) = P ( Z \leq -2.21371 )[/tex]
- Using standard normal table compute the probability on the left side of Z-score value -2.21371. Hence,
P ( X ≤ 26 ) = 0.0134
- The probability of the less than 26 number of cases who developed cancer of the brain or nervous system is 0.0134 as per media reports.
- So 1.34% of population is a case brain cancer due to cell phones according to media reports.
Which is significant less than the expected number of cases ( 40 ) that occur regardless of cell phone effect.
Answer: The significance of the cell phone causing brain cancer is 1.34 or 0.0134.
The time until recharge for a battery in a laptop computer under common conditions is normally distributed with mean of 265 minutes and a standard deviation of 50 minutes. a) What is the probability that a battery lasts more than four hours? Enter your answer in accordance to the item a) of the question statement (Round the answer to 3 decimal places.) b) What are the quartiles (the 25% and 75% values) of battery life? 25% value = Enter your answer; 25% value = _ minutes minutes (Round the answer to the nearest integer.) 75% value = Enter your answer; 75% value = _ minutes minutes (Round the answer to the nearest integer.) c) What value of life in minutes is exceeded with 95% probability? Enter your answer in accordance to the item c) of the question statement (Round the answer to the nearest integer.)
Answer:
a) 0.691 = 69.1% probability that a battery lasts more than four hours
b) 25% value = 231
75% value = 299
c) 183 minutes
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
[tex]\mu = 265, \sigma = 50[/tex]
a) What is the probability that a battery lasts more than four hours?
4 hours = 4*60 = 240 minutes
This is 1 subtracted by the pvalue of Z when X = 240. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{240 - 265}{50}[/tex]
[tex]Z = -0.5[/tex]
[tex]Z = -0.5[/tex] has a pvalue of 0.309
1 - 0.309 = 0.691
0.691 = 69.1% probability that a battery lasts more than four hours
b) What are the quartiles (the 25% and 75% values) of battery life?
25th percentile:
X when Z has a pvalue of 0.25. So X when Z = -0.675
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-0.675 = \frac{X - 265}{50}[/tex]
[tex]X - 265 = -0.675*50[/tex]
[tex]X = 231[/tex]
75th percentile:
X when Z has a pvalue of 0.75. So X when Z = 0.675
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]0.675 = \frac{X - 265}{50}[/tex]
[tex]X - 265 = 0.675*50[/tex]
[tex]X = 299[/tex]
25% value = 231
75% value = 299
c) What value of life in minutes is exceeded with 95% probability?
The 100-95 = 5th percentile, which is the value of X when Z has a pvalue of 0.05. So X when Z = -1.645.
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]-1.645 = \frac{X - 265}{50}[/tex]
[tex]X - 265 = -1.645*50[/tex]
[tex]X = 183[/tex]
What is the value of 2 in 255.6
Answer:
200?
Step-by-step explanation:
its kinda simple but the 2 is in the hundreds place therefore it is 200.
hope it helped ;)
Shiffon Electronics manufactures music player. Its costing system uses two cost categories, direct materials and conversion costs. Each product must pass through the Assembly Department, the Programming department, and the Testing Department. Direct materials are added at the beginning of the production process. Conversion costs are allocated evenly throughout production. Shiffon Electronics uses weighted-average costing. The following information is available for the month of March 2017 for the Assembly department. Work in process, beginning inventory 340 units Conversion costs (25% complete) Units started during March 860 units Work in process, ending inventory: 140 units Conversion costs (60% complete) The cost details for the month of March are as follows: Work in process, beginning inventory: Direct materials $349,000 Conversion costs $360,000 Direct materials costs added during March $703,500 Conversion costs added during March $1,130,000 What amount of conversion costs is assigned to the ending Work-in-Process account for March
Answer:
Possible options:
A.$182,343
B.$122,792
C.$109,406
D.$270,629
Answer C
Step-by-step explanation:
Under this method the percentage completion done in the Beginning Inventory is ignored while calculating the equivalent completed units during the current period. Beginning Inventory Units are treated as fresh units introduced for production.
Cost Accounted for:
- The cost of opening work-in-progress and cost of the current period are aggregated and the aggregate cost is divided by output in terms of completed equivalent units.
- The units of Beginning Inventory of WIP and their cost are taken in full under this method.
The owner of the pizza chain wants to monitor the total weight of pepperoni. Suppose that for pizzas in this population, the weights have a mean of 250g and a standard deviation of 4g. Management takes a random sample of 64 of these pizzas and calculates the mean weight of the pepperoni on the pizzas. Assume that the pizzas in the sample are independent. What is the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251g
Answer:
The probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is 0.02275.
Step-by-step explanation:
We are given that the owner of the pizza chain wants to monitor the total weight of pepperoni. Suppose that for pizzas in this population, the weights have a mean of 250 g and a standard deviation of 4 g.
Management takes a random sample of 64 of these pizzas.
Let [tex]\bar X[/tex] = sample mean weight of the pepperoni.
The z score probability distribution for sample mean is given by;
Z = [tex]\frac{X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean weight = 250 g
[tex]\sigma[/tex] = standard deviation = 4 g
n = sample of pizzas = 64
Now, the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is given by = P([tex]\bar X[/tex] > 251 g)
P([tex]\bar X[/tex] > 251 g) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{251-250}{\frac{4}{\sqrt{64} } }[/tex] ) = P(Z > 2) = 1 - P(Z [tex]\leq[/tex] 2)
= 1 - 0.97725 = 0.02275
The above probabilities is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.
Hence, the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is 0.02275.